I don't understand why apologizing is seen by some people as loss of face; surely you only really lose face when you don't apologize. Anyway, another form of non-apology is distracting the aggrieved person with twinkling objects. With luck, and if it's carried out with enough charm, it smoothes things over.

Laurent C said,

The advice of speaking slowly to a foreigner is not that bad – provided they know a little bit of your language. Some native speakers will only speak louder, as if they talked to a hearing-impaired person. This is really useless.

Bloix said,

Das machte meinen Abend: How to Apologize When You're Not Sure What You Did……

Basic Instructions: How to Apologize When You're Not Sure What You Did…
The Art of the (Non-) Apology
[via Language Log]
Wie der großartige Randy Pausch zu berichten wusste:
"Proper apologies have three parts: 1. What I did …

[…] that the speaker was a representative from South Carolina, who offered an actual apology (not a non-apology) for this breach of respect, only to say later that he'd done it because his party leadership […]